I can’t decide which of these two books I should start reading. They are structured very differently so it’s hard to compare them before reading them. Can anyone fill me in on there experience with these books or maybe what things one has that the other doesn’t.
Rigorous multi variable calc would be on the level of Spivak Calculus on Manifolds or Munkres Analysis on Manifolds. Are you sure you want rigour for a first course?
Undergrad Vector Calc is almost exclusively integral and derivatives and combining them in those theorems. You should make sure you are comfortable with partial derivatives, iterated integrals, and vector operations like dot product and cross product. The book you mention probably won't be much...
I'm looking for a good Complex book, but the options seem slim. I was thinking about Rudin's Real and Complex. My only reservation is that it is not structured like any other book I've seen. I've had advanced analysis and measure and integration theory, so rigour is not a concern. I saw Alfohr's...
You need everything from pre-cal. Depending on the rigor of your course, you could probably do without sequences and series. Cal 3 is not like Cal 1 and Cal 2 in the respect that cal 1 was only differential calculus and cal 2 was only integral calculus (possibly series). Cal 3 is all of the...
I think all of the branches of math can be somewhat separated from each other (although they all use set theory and logic at their core), but that is a very dry way of thinking about it. The most beautiful parts of mathematics, I think, is when you can apply all of those areas together...
"Gaps" may not have been the best wording, but he is trying to convey that the rational numbers are lacking "something". In this example, you see that you can get very close to root 2, indeed arbitrarily close to root 2, but we both know root 2 is not rational, so the rationals are lacking...
I would like to learn differential geometry the mathematicians way, not the physicists way. I usually just gloss over passages about Hausdorff spaces, second countable, paracompact and things of that nature and I would like to stop doing that.
I would like to know which chapters in Munkres Topology textbook are essential for a physicist. My background in topology is limited to the topology in baby Rudin, Kreyzig's functional, and handwavy topology in intro GR books. I feel like the entire book isn't necessary, but I could be mistaken.
It was known to Maxwell that the fields carry momentum. In fact, most EM books derive the radiation pressure formulas right after deriving the Field Momentum formulas. The momentum is also in the same direction as the Poynting vector.